The number of days needed in repairing a house varies inversely as the number of men working. It takes 15 days for 2 men to repair the house. How many men are needed to complete the job in 6 days?
Question
The number of days needed in repairing a house varies inversely as the number of men working. It takes 15 days for 2 men to repair the house. How many men are needed to complete the job in 6 days?
Solution
Let's solve this problem step by step:
Step 1: Identify the given information:
- It takes 15 days for 2 men to repair the house.
Step 2: Set up the inverse variation equation: Let d be the number of days needed to repair the house, and let m be the number of men working. According to the problem, the number of days needed varies inversely with the number of men working. Therefore, we can write the equation as: d = k/m, where k is the constant of variation.
Step 3: Find the value of k: To find the value of k, we can use the given information. We know that it takes 15 days for 2 men to repair the house. Substituting these values into the equation, we get: 15 = k/2 Solving for k, we multiply both sides by 2: k = 30
Step 4: Use the equation to find the number of men needed to complete the job in 6 days: We want to find the number of men needed to complete the job in 6 days. Let's call this number x. Substituting the values into the equation, we get: 6 = 30/x Solving for x, we multiply both sides by x: 6x = 30 Dividing both sides by 6, we get: x = 5
Therefore, 5 men are needed to complete the job in 6 days.
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